Integralne jednadžbe i primjene

master's thesis

• Author: Helena Frančešević
• Mentor: Igor Pažanin (mentor)
• Committee member: Igor Pažanin (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu bavimo se integralnim jednadžbama i njihovim primjenama. Integralne jednadžbe su jednadžbe kod kojih se nepoznata funkcija, koju trebamo odrediti, pojavljuje pod znakom integrala. Integralne jednadžbe su jedan od korisnijih matematičkih alata u teoretskoj i primijenjenoj matematici te imaju značajnu primjenu u mnogim fizikalnim problemima. Rad se sastoji od četiri poglavlja. U Poglavlju 1 bavimo se konceptom integralnih jednadžbi, njihovom povijesnom pozadinom te donosimo njihovu klasifikaciju. U Poglavlju 2 obratili smo posebnu pozornost na Volterrine integralne jednadžbe i različite metode njihovog rješavanja. U Poglavlju 3 fokusirali smo se na Fredholmove integralne jednadžbe i pripadajuće tehnike rješavanja. U posljednjem, Poglavlju 4 kao dodatak obradili smo Laplaceove transformacije i osnovna svojstva koja smo primjenjivali u glavnom dijelu rada.

Abstract (english)

In this work we deal with the integral equations and their applications. Integral equation is an equation in which the unknown function to be determined appear under the integral sign. Integral equations are one of the most useful mathematical tools in pure and applied mathematics, and are widely used in many physical problems. This work contains four chapters. In Chapter 1 we deal with the concept of integral equations, its historical background and classification. In Chapter 2 we have paid special attention to Volterra integral equations and the corresponding solving techniques. In chapter 3 we focused on the Fredholm integral equation and different solution methods. In the last, fourth, chapter written as a supplement we introduced Laplace transformations, and its basic properties that we applied in the main part of the work.

• Keywords: integralne jednadžbe; Volterrine integralne jednadžbe; Fredholmove integralne jednadžbe; Laplaceove transformacije
• Keywords (english): integral equations; Volterra integral equations; Fredholm integral equation; Laplace transformations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:994925
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-01-22 12:05:39